An Earth satellite is moved from one stable circular orbit to a farthe...
Explanation:
When an Earth satellite is moved from one stable circular orbit to a farther stable circular orbit, its distance from the Earth increases. This means that the gravitational potential energy of the satellite also increases. Let's see how each of the given options is affected by this change:
a) Linear orbit speed: The linear orbit speed of a satellite in a circular orbit depends only on the mass of the primary body (Earth) and the radius of the orbit. It is given by the formula v = √(GM/R), where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the orbit. As the radius of the orbit increases, the linear orbit speed decreases according to this formula. Hence, option 'a' is incorrect.
b) Gravitational force: The gravitational force between two objects depends on their masses and the distance between them. As the distance between the satellite and the Earth increases, the gravitational force between them decreases according to the inverse square law. Hence, option 'b' is incorrect.
c) Centripetal acceleration: The centripetal acceleration of a satellite in a circular orbit depends only on the mass of the primary body (Earth) and the radius of the orbit. It is given by the formula a = v²/R = GM/R², where v is the linear orbit speed. As we have seen earlier, the linear orbit speed decreases as the radius of the orbit increases, but the radius also increases. Hence, it is not clear whether the centripetal acceleration increases or decreases. Hence, option 'c' is incorrect.
d) Gravitational potential energy: The gravitational potential energy of a satellite in a circular orbit depends on its mass, the mass of the primary body (Earth), and the distance between them. It is given by the formula U = -GMm/R, where m is the mass of the satellite. As the distance between the satellite and the Earth increases, the gravitational potential energy of the satellite increases according to this formula. Hence, option 'd' is correct.
Conclusion:
When an Earth satellite is moved from one stable circular orbit to a farther stable circular orbit, its gravitational potential energy increases, while its linear orbit speed, gravitational force, and centripetal acceleration may increase or decrease depending on the radius of the new orbit.
An Earth satellite is moved from one stable circular orbit to a farthe...
Gravitational potential energy is given as,
Therefore, the gravitational potential energy increases.
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